### Root of a complex number

The **root of a complex number** must be reduced to an arithmetic root in order to calculate it, with

##### Explanation

Complex numbers can be converted by using the definition of the imaginary unit *i*^{ 2} = – 1. You then no longer have a minus sign. With a multiplication you get

where *a* and *b* are positive numbers.

##### Example 1

The result of the calculation

yields a negative number, and I'm sure you didn't expect that to happen. So it's not

##### Example 2

The calculation

is wrong. The feature

applies only to arithmetic roots. Algebraic roots must first be reduced to arithmetic roots.